Endmill specification design method, cutting condition detecting method, and processing method

ABSTRACT

Provided is an endmill (5). The maximum spindle speed, per one minute, of a main spindle to which the endmill is attached is Smax. The number of teeth of the endmill (5) is N. The outer shape of the endmill (5) is Da. The natural frequency at which vibrations at the end of the endmill (5) reach a maximum level is ω1. ω1 and/or N are set so that when the diameter-direction infeed amount of the endmill (5) is set to Rd: i) ω1×60/N×6&lt;Smax, if Rd is at least 4% of Da; and ii) ω1×60/N×3&lt;Smax, if Rd is less than 4% of Da.

TECHNICAL FIELD

The present invention relates to an endmill specification design method,a cutting condition detecting method, and a processing method.

BACKGROUND ART

In recent years, aircraft structural components are progressivelyintegrated with each other, and component shapes thereof are morecomplicated. A product height increases. Consequently, there is anincreasing need for shape processing using a protruding long toolprotruding beyond L/D (overhang length/diameter)=5. These componentsbecome joint parts as primary structural members in many cases.Accordingly, processed surface characteristics of the components areimportant. However, the protruding long tool has a problem of aregenerative chatter vibration generated on the tool side, therebycausing a problem in that a processed surface may be defective and aprocessing time may be lengthened. In general, rigidity is proportionalto the cube of a protrusion amount. Accordingly, when the components areprocessed using the long tool, a worker uses a stable pocket serving asa rotation speed region which can avoid the regenerative chattervibration. In this manner, the worker further reduces a load as much aspossible. Therefore, the processing time is extremely lengthened.Moreover, since one surface is processed in multiple paths, a mismatchoccurs between the paths. Accordingly, hand finishing is required afterthe surface is processed. In addition, the stable pocket is an integralfraction of natural vibration frequencies. Accordingly, as the rigidityis lowered (as natural vibration is small), rotation speed is lowered,thereby degrading efficiency.

In order to cope with this problem, the following processing methodcalled single finishing has been recently promoted. In a case of sidesurface finishing, a side surface is finished in one step. However, thisprocessing also has the following problems.

-   -   Large vibration is generated due to large axial cutting.    -   A stable region is narrowed and becomes unstable since a tool        having a long overhang length has low damping performance.    -   Since the rigidity is weak, the tool is fallen down as much as        0.1 mm or longer. Accordingly, quick feeding is not available.

In addition, in a case of bottom surface finishing for a deep pocket,processing is performed using a whole diameter of the tool. Accordingly,the chatter vibration is likely to be generated. Therefore, cutting isgenerally performed by reducing radial cutting or feeding.

In view of these circumstances, as a tool which is less likely tovibrate, there are provided some inventions and products relating to atooth shape. However, tool manufacturers in the related art haveinsufficient viewpoints of vibration characteristics. Therefore,dedicated tools have narrow application conditions. The single finishingis very unstable, and a user has difficulties in using the singlefinishing.

PTL 1 discloses a processing method of an endmill focusing on vibrationcharacteristics. That is, PTL 1 discloses a method of using an effect(process damping) in which a tool and a workpiece are damped by cominginto contact with each other during processing in a case of low-speedcutting.

CITATION LIST Patent Literature

[PTL 1] Specification of U.S. Pat. No. 8,875,367

SUMMARY OF INVENTION Technical Problem

However, according to PTL 1, the natural frequency is raised throughweight reduction of the tool so that the process damping in a low-speedregion is used in a medium-speed region. Consequently, there is alimitation in further using the process damping in a high-speed region.

In view of these problems, the present disclosure aims to performprocessing by stably using an endmill at a high speed.

Solution to Problem

According to an aspect of the present invention, there is provided anendmill specification design method including setting ω1 and/or N so asto satisfy the following. When a maximum spindle speed per one minute ofa main spindle having an endmill attached thereto is defined as Smax,the number of teeth of the endmill is defined as N, an outer shape ofthe endmill is defined as Da, a natural frequency at which a vibrationis maximized in a tool tip of the endmill is defined as ω1, and a radialdepth of cut of the endmill is defined as Rd, i) in a case where Rd isequal to or greater than 4% of Da, ω1×60/N×6<Smax is satisfied, and ii)in a case where Rd is smaller than 4% of Da, ω1×60/N×3<Smax issatisfied.

A stable spindle speed at which the endmill can stably perform machiningwithout generating a regenerative chatter vibration is defined asω1×60/N/n (n is a natural number). Through examinations, the presentinventor has found that the rotation speed higher than a first stablespindle speed at which n is defined as 1 also has a wide stable region.Then, this stable region is changed by the radial depth of cut Rd of theendmill. Therefore, ω1 and/or N are set so as to satisfy the following.

i) In a case where Rd is equal to or greater than 4% of Da,ω1×60/N×6<Smax is satisfied.

ii) In a case where Rd is smaller than 4% of Da, ω1×60/N×2<Smax issatisfied.

In this manner, the main spindle can be increased to the rotation speedclose to the maximum spindle speed Smax, and high speed and stablemachining can be performed. For example, the natural frequency ω1 isdecreased by increasing a protrusion amount of the endmill. The firststable spindle speed is decreased by increasing the number of teeth N.In this manner, a stable region having a higher rotation speed than thefirst stable spindle speed can be widely used.

In the endmill specification design method according to the aspect ofthe present invention, bottom surface machining may be performed in acase of i), and side surface machining may be performed in a case ofii).

In the case of i), the radial depth of cut is larger than that in thecase of ii). Accordingly, the case of i) is suitable for bottom surfacemachining in pocket processing, particularly for bottom surfacefinishing in deep pocket processing. In the case of ii), the radialdepth of cut is smaller than that in the case of i). Accordingly, thecase of i) is suitable for side surface machining, particularly forsingle finishing processing in

According to another aspect of the present invention, there is provideda cutting condition detecting method including setting a rotation speedof a main spindle having an endmill attached thereto so as to satisfythe following. When a maximum spindle speed per one minute of the mainspindle is defined as Smax, the number of teeth of the endmill isdefined as N, an outer shape of the endmill is defined as Da, a naturalfrequency at which a vibration is maximized in a tool tip of the endmillis defined as ω1, and a radial depth of cut of the endmill is defined asRd, i) in a case where Rd is equal to or greater than 4% of Da, a rangeof ω1×60/N×6 to Smax is satisfied, and ii) in a case where Rd is smallerthan 4% of Da, a range of ω1×60/N×3 to Smax is satisfied.

The stable spindle speed at which the endmill can stably perform themachining without generating the regenerative chatter vibration isω1×60/N/n (n is a natural number). Through examinations, the presentinventor has found that the rotation speed higher than the first stablespindle speed at which n is defined as 1 also has the wide stableregion. Then, this stable region is changed by the radial depth of cutRd of the endmill.

Therefore, the rotation speed of the main spindle is set so as tosatisfy the following.

i) In a case where Rd is equal to or greater than 4% of Da, a range ofω1×60/N×6 to Smax is satisfied.

ii) In a case where Rd is smaller than 4% of Da, a range of ω1×60/N×3 toSmax is satisfied.

In this manner, a workpiece can be processed at the rotation speedhigher than the first stable spindle speed, and the machining can bestably performed at high speed.

In the cutting condition detecting method according to the aspect of thepresent invention, bottom surface machining may be performed in a caseof i), and side surface machining may be performed in a case of ii).

In the case of i), the radial depth of cut is larger than that in thecase of ii). Accordingly, the case of i) is suitable for the bottomsurface machining in the pocket processing, particularly for the bottomsurface finishing in the deep pocket processing. In the case of ii), theradial depth of cut is smaller than that in the case of i). Accordingly,the case of ii) is suitable for the side surface machining, particularlyfor the single finishing processing in the deep axial cutting of theendmill.

In the cutting condition detecting method according to the aspect of thepresent invention, the rotation speed of the main spindle is set to arotation speed so as to avoid ω′×60/N(m−0.5) (m is a natural number),when the natural frequency that is a frequency higher than ω1 serving asthe natural frequency at which the vibration is maximized in the tooltip of the endmill, that has a vibration peak independent of ω1, andthat has a peak value of the vibration which is equal to or greater than1/10 of a peak value of ω1 is defined as ω′.

When the natural frequency that is a frequency higher than ω1 serving asthe natural frequency at which the vibration is maximized in the tooltip of the endmill, that has a vibration peak independent of ω1, andthat has a peak value of the vibration which is equal to or greater than1/10 of a peak value of ω1 is defined as ω′, the stable spindle speed isalso set as ω′×60/N/n for ω′ (n is a natural number). Since ω′ has thefrequency higher than ω1, the stable spindle speed of ω′ may appear atthe frequency higher than ω1 in some cases. On the other hand, theregenerative chatter vibration appears between the adjacent stablespindle speeds (for example, between m=1 and 2). Therefore, a medianvalue that may be an unstable region between the adjacent stable spindlespeeds of ω′ can be expressed by ω′×60/N(m−0.5). The rotation speed ofthe main spindle is set so as to avoid the median value. In this manner,the workpiece can be more stably processed.

According to still another aspect of the present invention, there isprovided a processing method including performing machining on aworkpiece by using any one of the cutting condition detecting methods.

The workpiece can be stably processed at high speed by using theabove-described cutting condition detecting method. For example, in acase of the bottom surface finishing, an axial cutting amount is set to1 mm or smaller, and a feeding amount per one tooth is set to 0.1mm/tooth or smaller. In a case of the side surface finishing, thefeeding amount per one tooth is set to 0.03 to 0.05 mm/tooth, and theaxial cutting amount is set to a length corresponding to the protrusionamount of the endmill. Therefore, a single tool can cope with processingfor workpieces having various depths. The above-described cuttingamounts or feeding amounts are merely examples, and can be obtainedthrough simulation or processing tests.

Advantageous Effects of Invention

The workpiece can be stably processed at high speed by using theendmill.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic configuration diagram illustrating an endmillaccording to an embodiment of the present invention.

FIG. 2 is a graph illustrating a stable pocket.

FIG. 3 is a graph illustrating a stable region existing on a rotationspeed higher than that of the stable pocket in FIG. 2.

FIG. 4 is a graph illustrating a ratio of each stable spindle speed to aradial depth of cut.

FIG. 5 is a graph illustrating vibration response characteristics of atool tip of the endmill.

FIG. 6 is a graph illustrating the stable region for two vibrationpeaks.

DESCRIPTION OF EMBODIMENTS

As illustrated in FIG. 1, an endmill 10 has a shaft 14 extending in anaxial direction, and a plurality of teeth 15 disposed in an outerperiphery of the shaft 14. One end of the endmill 10 is attached to amain spindle 5 by using a fixing tool such as a chuck. The main spindle5 is connected to a rotary shaft of a machine tool (not illustrated),and is rotated at a predetermined rotation speed instructed by a controlunit. A maximum spindle speed Smax of the main spindle 5 is determineddepending on capacity of the machine tool, and is set to 10,000 to40,000 (rpm), for example.

A length from the main spindle 5 to a tool tip of the endmill 10 is setas an overhang length L. The overhang length L is set to be changed inaccordance with processing conditions. The endmill 10 is mainly used inprocessing aluminum alloy, and is used in performing pocket processingon a member having a thickness of 100 mm to 500 mm, for example. Forexample, specific processing targets include aircraft structuralcomponents (keel beams or main wing center beams). A ratio L/Da of theoverhang length L to a tool diameter Da of the endmill 10 is set to 5 orgreater.

The tool diameter Da of the endmill 10 is set to 16 mm to 25 mm, and thenumber of teeth N is set to 10 to 25.

In machining performed by the endmill 10, a stable spindle speed Sn atwhich the endmill 10 can stably perform the machining without generatinga regenerative chatter vibration is determined as the followingequation.

Sn=ω1×60/N/n [rpm]  (1)

ω1 is a natural frequency of the tool tip of the endmill 10, N is thenumber of teeth, and n is a natural number. For example, the naturalfrequency ω1 can be obtained by performing tapping on the endmill 10attached to the main spindle 5, and is a frequency indicating a largestvibration peak.

The rotation speed region within a predetermined range around the stablespindle speed Sn becomes the stable pocket. If the main spindle 5 isrotated inside the stable pocket, the regenerative chatter vibration canbe avoided.

FIG. 2 illustrates a plurality of the stable pockets. In the drawing, ahorizontal axis represents a main spindle rotation speed [rpm], and avertical axis represents a horizontal cutting amount [mm]. The stableregion is located below a curve, and an unstable region where theregenerative chatter vibration is generated is located above the curve.

The drawing illustrates a first stable pocket SP1 at a first stablespindle speed S1 defined as n=1 in Equation (1) above, a second stablepocket SP2 at a second stable spindle speed S2 defined as n=2, and athird stable pocket SP3 at a third stable spindle speed S3 defined asn=3. Each stable pocket is 1/n^(th) of the first stable pocket SP1(refer to Equation (1)).

In a case of using the stable pocket SP illustrated in FIG. 2, there areproblems as follows. In the endmill 10 where L/Da is 5 or greater, theoverhang length L is long. Accordingly, the natural frequency ω1decreases, and the main spindle rotation speed at which the stablepocket SP appears decreases. Therefore, the machining is less likely tobe performed at high speed. In addition, a rotation speed width of thestable pocket SP is narrowed. Accordingly, the rotation speed is lesslikely to be adjusted. In addition, as the natural frequency ω1decreases, the stable pocket SP is closer to the natural frequency ω1.Accordingly, a forced vibration is likely to be generated.

In contrast, the present inventor has found the following. Asillustrated in FIG. 3, a stable pocket where the regenerative chattervibration is not generated exists in a region exceeding the first stablepocket SP1 and further exceeding the natural frequency ω1. Thehorizontal axis represents the main spindle rotation speed [rpm], andthe vertical axis represents the horizontal cutting amount [mm]. Thestable region is located below a curve, and an unstable region where theregenerative chatter vibration is generated is located above the curve.

The drawing illustrates a simulation of the endmill 10 where the numberof teeth N is defined as 19, the tool diameter Da is defined as 25 mm,and the overhang length L is defined as 170 mm. This simulation isperformed using a stability limit analysis of the regenerative chattervibration in endmill processing, based on the above-described toolgeometry and frequency characteristics thereof.

As can be understood from the drawing, a first high-speed stable pocketSP1′ exists in a region of 6,000 [rpm] to 10,000 [rpm] which greatlyexceeds the first stable pocket SP1, and a large second high-speedstable pocket SP2′ exists in a region of 18,000 [rpm] or higher. Thepresent embodiment adopts the high-speed stable pockets SP1′ and SP2′.

Furthermore, the present inventor has found the following. A shape ofeach stable pocket SPs illustrated in FIG. 3 is changed depending on thenatural frequency ω1 and the radial depth of cut Rd [mm] of the endmill10. Therefore, the simulation is performed for various types of theendmill 10 by changing the natural frequency ω1 and the radial depth ofcut Rd. As a result, the present inventor has found that there is apredetermined relationship between the first stable spindle speed S1 andthe first high-speed stable spindle speed S1′ as illustrated in FIG. 4.

In FIG. 4, the horizontal axis represents Rd/Da [%], which is thepercentage of the radial depth of cut Rd to the tool diameter Da of theendmill 10, and the vertical axis represents a ratio of the firsthigh-speed stable spindle speed S1′ to the first stable spindle speedS1. As can be understood from the drawing, S1′/S1 is approximately 3 ina case where Rd/Da is smaller than 4%, and S1′/S1 is approximately 6 ina case where Rd/Da is equal to or greater than 4%. That is, the meaningis as follows. In the case where Rd/Da is smaller than 4%, the firsthigh-speed stable spindle speed S1′ exists around 3 times the firststable spindle speed S1. In the case where Rd/Da is equal to or greaterthan 4%, the first high-speed stable spindle speed S1′ exists around 6times the first stable spindle speed S1. If the first high-speed stablepocket SP1′ including the first high-speed stable spindle speed S1′ isused, the machining can be stably performed at high speed by using theendmill 10.

Next, referring to FIGS. 5 and 6, influence on a vibration peak of theendmill 10 at the frequency higher than the natural frequency ω1 will beexamined. The above-described natural frequency ω1 is the frequencywhich indicates the highest vibration peak in a case where the frequencyof the tool tip of the endmill 10 is analyzed. In some cases, thefrequency indicating an independent vibration peak may exist in thefrequency higher than the natural frequency ω1. Specifically, asillustrated in FIG. 5, in some cases, the independent vibration peak onthe frequency side higher than the natural frequency ω1 which is thefirst vibration peak may be recognized as a second peak frequency ω2. Asexpressed in Equation (1), the stable spindle speed also exists in thesecond peak frequency ω2, and an unstable region exists in a regionhaving no stable spindle speed. FIG. 6 illustrates a result of examiningthe stable region and the unstable region for the second peak frequencyω2.

In FIG. 6, the horizontal axis represents the main spindle rotationspeed [rpm], and the vertical axis represents the horizontal cuttingamount [mm]. The drawing illustrates a curve L1 indicating the stableregion corresponding to the natural frequency ω1, a curve L2 indicatingthe stable region corresponding to the second peak frequency ω2, and acurve L3 obtained by superimposing the curves L1 and L2 on each other.As can be understood from the drawing, a region where L3 is greatlyrecessed downward exists around 14000 [rpm] indicated by a line segmentL4. The reason is the influence caused by the curve L2 of the secondpeak frequency ω2. The rotation speed region indicated by the linesegment L4 is the unstable region. Accordingly, it is preferable toavoid the rotation speed region. Therefore, the main spindle rotationspeed is limited as follows.

The natural frequency that is a frequency higher than ω1 serving as thenatural frequency at which the vibration is maximized in the tool tip ofthe endmill 10, that has the vibration peak independent of the naturalfrequency ω1, and that has the peak value of the vibration which isequal to or greater than 1/10 of the peak value of ω1 is defined as ω′.It is assumed that the m-number of ω′ exists (m is a natural number). Inthis case, the rotation speed of the main spindle 5 is set so as to bethe rotation speed avoiding ω′×60/N/(m−0.5). In this manner, it ispossible to avoid the center rotation speed between the adjacent stablepockets.

Endmill Specification Design Method

Next, an endmill specification design method used based on theabove-described concept will be described. Smax represents the maximumspindle speed of the main spindle 5. ω1 and/or N are set so as tosatisfy (ω1×60/N×6<Smax, i) in a case where the radial depth of cut Rdis equal to or greater than 4% of the tool diameter Da, and so as tosatisfy ω1×60/N×3<Smax, ii) in a case where the radial depth of cut Rdis smaller than 4% of the tool diameter Da.

In this manner, the rotation speed can be increased up to the mainspindle rotation speed close to the maximum spindle speed Smax of themain spindle 5. Accordingly, the machining can be stably performed athigh speed. For example, the natural frequency ω1 is decreased byincreasing the protrusion amount of the endmill. The first stablespindle speed S1 is decreased by increasing the number of teeth N. Inthis manner, the first high-speed stable pocket SP1′ having the higherrotation speed than the first stable spindle speed S1 can be widelyused.

In this case, bottom surface machining is preferably performed in theabove-described case of i), and side surface machining is preferablyperformed in the above-described case of ii).

In the case of i), the radial depth of cut Rd is larger than that in thecase of ii). Accordingly, the case of i) is suitable for the bottomsurface machining in the pocket processing, particularly for the bottomsurface finishing in the deep pocket processing. In the case of ii), theradial depth of cut Rd is smaller than that in the case of i).Accordingly, the case of ii) is suitable for the side surface machining,particularly for the single finishing processing in the deep axialcutting of the endmill.

Cutting Condition Detecting Method

Next, a cutting condition detecting method used based on theabove-described concept will be described. Smax represents the maximumspindle speed of the main spindle 5. The rotation speed of the mainspindle 5 is set so as to satisfy a range of ω1×60/N×6 to Smax, i) in acase where the radial depth of cut Rd is equal to or greater than 4% ofthe tool diameter Da, and so as to satisfy a range of ω1×60/N×3 to Smax,ii) in a case where the radial depth of cut Rd is smaller than 4% of thetool diameter Da.

The processing conditions are set to the above-described conditions. Inthis manner, a workpiece can be processed in the first high-speed stablepocket SP1′ having the higher rotation speed than the first stablespindle speed S1. Therefore, the machining can be stably performed athigh speed.

In this case, bottom surface machining is preferably performed in theabove-described case of i), and side surface machining is preferablyperformed in the above-described case of ii).

In the case of i), the radial depth of cut Rd is larger than that in thecase of ii). Accordingly, the case of i) is suitable for the bottomsurface machining in the pocket processing, particularly for the bottomsurface finishing in the deep pocket processing. In the case of ii), theradial depth of cut Rd is smaller than that in the case of i).Accordingly, the case of ii) is suitable for the side surface machining,particularly for the single finishing processing in the deep axialcutting of the endmill.

Furthermore, it is preferable to add the following conditions when theprocessing conditions are set. The rotation speed of the main spindle 5is set so as to avoid ω+×60/N(m−0.5) (m is a natural number), when thenatural frequency that is the frequency higher than the naturalfrequency ω1 at which the vibration is maximized in the tool tip of theendmill 10, that has the vibration peak independent of ω1, and that hasthe peak value of the vibration which is equal to or greater than 1/10of the peak value of ω1 is defined as ω′.

Since ω′ has the frequency higher than ω1, the stable spindle speed ofω′ may appear at the frequency higher than ω1 in some cases. On theother hand, the regenerative chatter vibration appears between theadjacent stable spindle speeds (for example, between m=1 and 2) (referto FIG. 6). Therefore, a median value that may be an unstable regionbetween the adjacent stable spindle speeds of ω′ can be expressed byω+60/N(m−0.5). The rotation speed of the main spindle 5 is set so as toavoid the median value. In this manner, the processing can be morestably performed.

Processing Method

Next, a processing method used based on the above-described concept willbe described. As the processing method, the machining is performed usingthe endmill 10 under the conditions of the above-described cuttingcondition detecting method. In this case, the endmill 10 obtained basedon the above-described endmill specification design method is used. Inthis manner, the processing can be stably performed at high speed.

For example, in a case of the bottom surface finishing, the axialcutting amount is set to 1 mm or smaller, and the feeding amount per onetooth is set to 0.1 mm/tooth or smaller. In a case of the side surfacefinishing, the feeding amount per one tooth is set to 0.03 to 0.05mm/tooth, and the axial cutting amount is set to the lengthcorresponding to the protrusion amount of the endmill. Therefore, asingle tool can cope with processing for workpieces having variousdepths. The above-described cutting amounts or feeding amounts aremerely examples, and can be obtained through simulation or processingtests.

REFERENCE SIGNS LIST

-   5: main spindle-   10: endmill-   14: shaft-   15: tooth-   Da: tool diameter (of endmill)-   L: overhang length (of endmill)-   Smax: maximum spindle speed (of main spindle)-   Rd: radial depth of cut-   ω1: natural frequency (of endmill tool tip)-   S1: first stable spindle speed-   S1′: first high-speed stable spindle speed-   SP, SP1, SP2, SP3: stable pocket-   SP1′: first high-speed stable pocket-   SP2′: second high-speed stable pocket

1. An endmill specification design method, comprising: setting ω1 and/orN so as to satisfy the following, wherein when a maximum spindle speedper one minute of a main spindle having an endmill attached thereto isdefined as Smax, the number of teeth of the endmill is defined as N, anouter shape of the endmill is defined as Da, a natural frequency atwhich a vibration is maximized in a tool tip of the endmill is definedas ω1, and a radial depth of cut of the endmill is defined as Rd, i) ina case where Rd is equal to or greater than 4% of Da, ω1×60/N×6<Smax issatisfied, and ii) in a case where Rd is smaller than 4% of Da,ω1×60/N×3<Smax is satisfied.
 2. The endmill specification design methodaccording to claim 1, wherein bottom surface machining is performed in acase of i), and side surface machining is performed in a case of ii). 3.A cutting condition detecting method, comprising: setting a rotationspeed of a main spindle having an endmill attached thereto so as tosatisfy the following, wherein when a maximum spindle speed per oneminute of the main spindle is defined as Smax, the number of teeth ofthe endmill is defined as N, an outer shape of the endmill is defined asDa, a natural frequency at which a vibration is maximized in a tool tipof the endmill is defined as ω1, and a radial depth of cut of theendmill is defined as Rd, i) in a case where Rd is equal to or greaterthan 4% of Da, a range of ω1×60/N×6 to Smax is satisfied, and ii) in acase where Rd is smaller than 4% of Da, a range of ω1×60/N×3 to Smax issatisfied.
 4. The cutting condition detecting method according to claim3, wherein bottom surface machining is performed in a case of i), andside surface machining is performed in a case of ii).
 5. The cuttingcondition detecting method according to claim 3, wherein the rotationspeed of the main spindle is set to a rotation speed so as to avoidω′×60/N(m−0.5) (m is a natural number), when the natural frequency thatis a frequency higher than oil serving as the natural frequency at whichthe vibration is maximized in the tool tip of the endmill, that has avibration peak independent of ω1, and that has a peak value of thevibration which is equal to or greater than 1/10 of a peak value of ω1is defined as ω′.
 6. A processing method comprising: performingmachining on a workpiece by using the cutting condition detecting methodaccording to claim 3.